Finite Group Databasebeta

C42×#11758201 #29678485

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#11758201

Splittings

FittingC42×Q8×C61 ⋊ C2
SylowC61 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42C22⋊D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC42×Q8×C61C2
socleC23×C61C22×D4
prime radicalC22×D244C23
cosocleC22×C4×C61C24
hypercenterC42×Q8D61
hypocenterC61C42×SD16
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×Q8

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 168040);